Finite Group Databasebeta

← C2×#13076612 #14959890

Subgroups — C2×#13076612 #14959890

Order 2816.

4438 conjugacy classes of subgroups.

The subgroup lattice has 1052 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66935C211yesmaximal, characteristic, complemented
2C22×#66990C211yesmaximal, characteristic, complemented
3#13076612C2116yesmaximal, direct product factor
4C2×#10622565C211yesmaximal, characteristic, complemented
5C2×#10622287C211yesmaximal, characteristic, complemented
6C2×#10622606C211yesmaximal, characteristic, complemented
7C2×#10622285C211yesmaximal, characteristic, complemented
8C2×#10622604C211yesmaximal, characteristic, complemented
9C2×#10622574C211yesmaximal, characteristic, complemented
10C2×#10622574C211yesmaximal, characteristic, complemented
11C2×#10622572C211yesmaximal, characteristic, complemented
12C2×#10622573C211yesmaximal, characteristic, complemented
13C2×#10622573C211yesmaximal, characteristic, complemented
14C2×#10622836C211yesmaximal, characteristic, complemented
15C2×#10622568C211yesmaximal, characteristic, complemented
16C2×C11×#394C211yesmaximal, characteristic, complemented
17C25×D11C2211yescharacteristic
18C23×D4×C11C2211yescharacteristic
19C23×C22⋊D11C2211yescharacteristic
20C23×C22⋊D11C2211yescharacteristic
21C23×C22⋊D11C2211yescharacteristic
22C23×C22⋊D11C2211yescharacteristic, complemented
23C23×D44C2211yescharacteristic
24C23×D44C2211yescharacteristic
25C22×C11×C4⋊C4C2211yescharacteristic, complemented
26C22×C11×C22⋊C4C2211yescharacteristic
27C22×C11×C22⋊C4C2211yescharacteristic
28C22×C11×C22⋊C4C2211yescharacteristic, complemented
29C22×C11×C22⋊C4C2211yescharacteristic, complemented
30C22×C22⋊Dic11C2211yescharacteristic
31C22×C22⋊Dic11C2211yescharacteristic
32C22×C22⋊Dic11C2211yescharacteristic, complemented
33C2×#66990—28no—
34C2×#66990C2218yescomplemented
35C22×(C2×D11)⋊C4C2211yescharacteristic
36C22×(C2×D11)⋊C4C2211yescharacteristic
37C22×(C2×D11)⋊C4C2211yescharacteristic
38C22×(C2×D11)⋊C4C2211yescharacteristic
39C22×(C2×D11)⋊C4C2211yescharacteristic
40C22×(C2×D11)⋊C4C2211yescharacteristic
41C22×(C2×D11)⋊C4C2211yescharacteristic
42C22×(C2×D11)⋊C4C2211yescharacteristic
43C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
44C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
45C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
46C22×C4⋊Dic11C2211yescharacteristic, complemented
47C22×Dic11⋊C4C2211yescharacteristic, complemented
48C2×#66935—28no—
49C2×#66935C2218yescomplemented
50C11×#394C2218yescomplemented
51C2×C11×#95C2211yescharacteristic, complemented
52#10622836C2218yescomplemented
53C2×C11⋊#95C2211yescharacteristic, complemented
54C2×C11⋊#95C2211yescharacteristic, complemented
55C2×C11⋊#95C2211yescharacteristic, complemented
56C2×C11⋊#95C2211yescharacteristic, complemented
57C2×C11⋊#95C2211yescharacteristic, complemented
58#10622606C2218yescomplemented
59#10622604C2218yescomplemented
60#10622574C2218yescomplemented
61#10622574C2218yescomplemented
62#10622573C2218yescomplemented
63#10622573C2218yescomplemented
64#10622572C2218yescomplemented
65#10622568C2218yescomplemented
66#10622565C2218yescomplemented
67#10622287C2218yescomplemented
68#10622285C2218yescomplemented
69C25×C11C2311yescharacteristic
70C25×C11C2311yescharacteristic
71C24×D11—42no—
72C24×D11—42no—
73C24×D11—42no—
74C24×D11—42no—
75C24×D11—42no—
76C24×D11—42no—
77C24×D11D418yescomplemented
78C24×D11C2311yescharacteristic
79C24×D11C2311yescharacteristic
80C24×D11C2311yescharacteristic
81C24×D11C2314yes—
82C22×D4×C11—24no—
83C22×D4×C11—42no—
84C22×D4×C11—42no—
85C22×D4×C11C2314yes—
86C23×C4×C11C2311yescharacteristic
87C23×C4×C11C2311yescharacteristic
88C23×C4×C11C2311yescharacteristic
89C23×C4×C11C2311yescharacteristic
90C23×C4×C11C2311yescharacteristic
91C22×C22⋊D11—24no—
92C22×C22⋊D11—24no—
93C22×C22⋊D11—24no—
94C22×C22⋊D11—42no—
95C22×C22⋊D11—42no—
96C22×C22⋊D11—42no—
97C22×C22⋊D11—42no—
98C22×C22⋊D11—42no—
99C22×C22⋊D11—42no—
100C22×C22⋊D11—42no—
101C22×C22⋊D11—42no—
102C22×C22⋊D11—42no—
103C22×C22⋊D11C2314yes—
104C22×C22⋊D11C2314yes—
105C22×C22⋊D11C2314yes—
106C22×C22⋊D11C2314yescomplemented
107C23×Dic11C2311yescharacteristic
108C23×Dic11C2311yescharacteristic
109C23×Dic11C2311yescharacteristic
110C23×Dic11C2311yescharacteristic
111C23×Dic11C2311yescharacteristic
112C22×D44—24no—
113C22×D44—24no—
114C22×D44—42no—
115C22×D44—42no—
116C22×D44—42no—
117C22×D44—42no—
118C22×D44C2314yes—
119C22×D44C2314yes—
120C2×C11×C4⋊C4—42no—
121C2×C11×C4⋊C4C2314yescomplemented
122C2×C11×C22⋊C4—24no—
123C2×C11×C22⋊C4—42no—
124C2×C11×C22⋊C4—42no—
125C2×C11×C22⋊C4—42no—
126C2×C11×C22⋊C4C2314yes—
127C2×C11×C22⋊C4C2314yes—
128C2×C11×C22⋊C4C2314yescomplemented
129C2×C11×C22⋊C4C2314yescomplemented
130C2×C22⋊Dic11—24no—
131C2×C22⋊Dic11—42no—
132C2×C22⋊Dic11—42no—
133C2×C22⋊Dic11C2314yes—
134C2×C22⋊Dic11C2314yes—
135C2×C22⋊Dic11C2314yescomplemented
136#66990—232no—
137C2×(C2×D11)⋊C4—24no—
138C2×(C2×D11)⋊C4—24no—
139C2×(C2×D11)⋊C4—24no—
140C2×(C2×D11)⋊C4—24no—
141C2×(C2×D11)⋊C4—42no—
142C2×(C2×D11)⋊C4—42no—
143C2×(C2×D11)⋊C4—42no—
144C2×(C2×D11)⋊C4—42no—
145C2×(C2×D11)⋊C4—42no—
146C2×(C2×D11)⋊C4—42no—
147C2×(C2×D11)⋊C4—42no—
148C2×(C2×D11)⋊C4C2314yes—
149C2×(C2×D11)⋊C4C2314yes—
150C2×(C2×D11)⋊C4C2314yes—
151C2×(C2×D11)⋊C4C2314yes—
152C2×(C2×D11)⋊C4C2314yes—
153C2×(C2×D11)⋊C4C2314yes—
154C2×(C2×D11)⋊C4C2314yes—
155C2×(C2×D11)⋊C4C2314yes—
156C2×(C2×D11)⋊C4C2314yescomplemented
157C2×(C2×D11)⋊C4C2314yescomplemented
158C2×(C2×D11)⋊C4C2314yescomplemented
159C2×C4⋊Dic11—42no—
160C2×C4⋊Dic11C2314yescomplemented
161C2×Dic11⋊C4—42no—
162C2×Dic11⋊C4C2314yescomplemented
163#66935—232no—
164C11×#95C2314yescomplemented
165C11⋊#95C2314yescomplemented
166C11⋊#95C2314yescomplemented
167C11⋊#95C2314yescomplemented
168C11⋊#95C2314yescomplemented
169C11⋊#95C2314yescomplemented
170C2×#2812—111nomaximal, Sylow
171C24×C11—22no—
172C24×C11—22no—
173C24×C11—22no—
174C24×C11—22no—
175C24×C11—22no—
176C24×C11—22no—
177C24×C11—22no—
178C24×C11—22no—
179C24×C11—22no—
180C24×C11—22no—
181C24×C11—22no—
182C24×C11—22no—
183C24×C11—22no—
184C24×C11C2×D414yes—
185C24×C11C2412yes—
186C24×C11C2412yes—
187C24×C11C2411yescharacteristic
188C23×D11—22no—
189C23×D11—22no—
190C23×D11—22no—
191C23×D11—22no—
192C23×D11—22no—
193C23×D11—22no—
194C23×D11—22no—
195C23×D11—22no—
196C23×D11—22no—
197C23×D11—22no—
198C23×D11—22no—
199C23×D11—22no—
200C23×D11—22no—
201C23×D11—22no—
202C23×D11—22no—
203C23×D11—22no—
204C23×D11—22no—
205C23×D11—22no—
206C23×D11—22no—
207C23×D11—416no—
208C23×D11—416no—
209C23×D11—416no—
210C23×D11—44no—
211C23×D11—44no—
212C23×D11—44no—
213C23×D11—44no—
214C23×D11—44no—
215C23×D11—44no—
216C23×D11—416no—
217C23×D11—416no—
218C23×D11—416no—
219C23×D11—416no—
220C23×D11C2×D414yes—
221C23×D11C2×D414yes—
222C23×D11C2×D4116yescomplemented
223C23×D11C2412yes—
224C23×D11C2412yes—
225C23×D11C2412yes—
226C2×D4×C11—28no—
227C2×D4×C11—44no—
228C2×D4×C11—44no—
229C2×D4×C11—416no—
230C22×C4×C11—22no—
231C22×C4×C11—22no—
232C22×C4×C11—22no—
233C22×C4×C11—22no—
234C22×C4×C11—22no—
235C22×C4×C11—22no—
236C22×C4×C11—22no—
237C22×C4×C11—22no—
238C22×C4×C11—22no—
239C22×C4×C11—22no—
240C22×C4×C11—22no—
241C22×C4×C11—22no—
242C22×C4×C11—22no—
243C22×C4×C11—22no—
244C22×C4×C11—22no—
245C22×C4×C11C2412yes—
246C22×C4×C11C2412yes—
247C22×C4×C11C2412yes—
248C22×C4×C11C2412yes—
249C22×C4×C11C2412yes—
250C2×C22⋊D11—28no—
251C2×C22⋊D11—28no—
252C2×C22⋊D11—28no—
253C2×C22⋊D11—44no—
254C2×C22⋊D11—44no—
255C2×C22⋊D11—44no—
256C2×C22⋊D11—44no—
257C2×C22⋊D11—44no—
258C2×C22⋊D11—44no—
259C2×C22⋊D11—44no—
260C2×C22⋊D11—44no—
261C2×C22⋊D11—44no—
262C2×C22⋊D11—416no—
263C2×C22⋊D11—416no—
264C2×C22⋊D11—416no—
265C2×C22⋊D11—416no—
266C22×Dic11—22no—
267C22×Dic11—22no—
268C22×Dic11—22no—
269C22×Dic11—22no—
270C22×Dic11—22no—
271C22×Dic11—22no—
272C22×Dic11—22no—
273C22×Dic11—22no—
274C22×Dic11—22no—
275C22×Dic11—22no—
276C22×Dic11—22no—
277C22×Dic11—22no—
278C22×Dic11—22no—
279C22×Dic11—22no—
280C22×Dic11—22no—
281C22×Dic11C2412yes—
282C22×Dic11C2412yes—
283C22×Dic11C2412yes—
284C22×Dic11C2412yes—
285C22×Dic11C2412yes—
286C2×D44—28no—
287C2×D44—28no—
288C2×D44—44no—
289C2×D44—44no—
290C2×D44—44no—
291C2×D44—44no—
292C2×D44—416no—
293C2×D44—416no—
294C11×C4⋊C4—44no—
295C11×C22⋊C4—28no—
296C11×C22⋊C4—44no—
297C11×C22⋊C4—44no—
298C11×C22⋊C4—44no—
299C22⋊Dic11—28no—
300C22⋊Dic11—44no—
301C22⋊Dic11—44no—
302(C2×D11)⋊C4—28no—
303(C2×D11)⋊C4—28no—
304(C2×D11)⋊C4—28no—
305(C2×D11)⋊C4—28no—
306(C2×D11)⋊C4—44no—
307(C2×D11)⋊C4—44no—
308(C2×D11)⋊C4—44no—
309(C2×D11)⋊C4—44no—
310(C2×D11)⋊C4—44no—
311(C2×D11)⋊C4—44no—
312(C2×D11)⋊C4—44no—
313C4⋊Dic11—44no—
314Dic11⋊C4—44no—
315C22×#120—111no—
316C22×#120—111no—
317#2812—1116no—
318C2×#397—111no—
319C2×#397—111no—
320C2×#397—111no—
321C2×#394—111no—
322C2×#394—111no—
323C2×#394—111no—
324C2×#394—111no—
325C2×#394—111no—
326C2×#394D1111yescharacteristic, complemented
327C2×#392—111no—
328C2×#392—111no—
329C2×#392—111no—
330C2×#379—111no—
331C23×C11—28no—
332C23×C11—28no—
333C23×C11—28no—
334C23×C11—22no—
335C23×C11—22no—
336C23×C11—22no—
337C23×C11—22no—
338C23×C11—22no—
339C23×C11—22no—
340C23×C11—22no—
341C23×C11—22no—
342C23×C11—22no—
343C23×C11—22no—
344C23×C11—22no—
345C23×C11—22no—
346C23×C11—22no—
347C23×C11—44no—
348C23×C11—44no—
349C23×C11—44no—
350C23×C11—44no—
351C23×C11—44no—
352C23×C11—44no—
353C23×C11—44no—
354C23×C11—44no—
355C23×C11—44no—
356C23×C11—44no—
357C23×C11—44no—
358C23×C11C22×D414yes—
359C23×C11C22×D412yes—
360C23×C11H(5,𝔽2)12yes—
361C23×C11H(5,𝔽2)12yes—
362C23×C11H(5,𝔽2)12yes—
363C23×C11H(5,𝔽2)12yes—
364C23×C11H(5,𝔽2)12yes—
365C23×C11H(5,𝔽2)12yes—
366C23×C11C2511yescharacteristic
367C22×D11—28no—
368C22×D11—28no—
369C22×D11—28no—
370C22×D11—28no—
371C22×D11—28no—
372C22×D11—28no—
373C22×D11—22no—
374C22×D11—22no—
375C22×D11—22no—
376C22×D11—22no—
377C22×D11—22no—
378C22×D11—22no—
379C22×D11—22no—
380C22×D11—22no—
381C22×D11—22no—
382C22×D11—22no—
383C22×D11—22no—
384C22×D11—22no—
385C22×D11—22no—
386C22×D11—22no—
387C22×D11—22no—
388C22×D11—22no—
389C22×D11—22no—
390C22×D11—22no—
391C22×D11—22no—
392C22×D11—416no—
393C22×D11—416no—
394C22×D11—416no—
395C22×D11—416no—
396C22×D11—416no—
397C22×D11—416no—
398C22×D11—416no—
399C22×D11—4128no—
400C22×D11—44no—
401C22×D11—44no—
402C22×D11—44no—
403C22×D11—44no—
404C22×D11—44no—
405C22×D11—44no—
406C22×D11—44no—
407C22×D11—44no—
408C22×D11—44no—
409C22×D11—44no—
410C22×D11—44no—
411C22×D11—44no—
412C22×D11—44no—
413C22×D11—44no—
414C22×D11—44no—
415C22×D11C22×D414yes—
416C22×D11C22×D414yes—
417D4×C11—416no—
418C2×C4×C11—22no—
419C2×C4×C11—22no—
420C2×C4×C11—22no—
421C2×C4×C11—22no—
422C2×C4×C11—22no—
423C2×C4×C11—22no—
424C2×C4×C11—22no—
425C2×C4×C11—22no—
426C2×C4×C11—22no—
427C2×C4×C11—22no—
428C2×C4×C11—22no—
429C2×C4×C11—22no—
430C2×C4×C11—22no—
431C2×C4×C11—22no—
432C2×C4×C11—22no—
433C2×C4×C11—44no—
434C2×C4×C11—44no—
435C2×C4×C11—44no—
436C2×C4×C11—44no—
437C2×C4×C11—44no—
438C22⋊D11—416no—
439C22⋊D11—416no—
440C22⋊D11—416no—
441C22⋊D11—416no—
442C2×Dic11—22no—
443C2×Dic11—22no—
444C2×Dic11—22no—
445C2×Dic11—22no—
446C2×Dic11—22no—
447C2×Dic11—22no—
448C2×Dic11—22no—
449C2×Dic11—22no—
450C2×Dic11—22no—
451C2×Dic11—22no—
452C2×Dic11—22no—
453C2×Dic11—22no—
454C2×Dic11—22no—
455C2×Dic11—22no—
456C2×Dic11—22no—
457C2×Dic11—44no—
458C2×Dic11—44no—
459C2×Dic11—44no—
460C2×Dic11—44no—
461C2×Dic11—44no—
462D44—416no—
463D44—416no—
464C26—111no—
465C23×D4—111no—
466C23×D4—111no—
467C23×D4—111no—
468C23×D4—111no—
469C23×D4—111no—
470C23×D4—111no—
471C23×D4C2×D1111yescharacteristic
472C2×#120—118no—
473C2×#120—118no—
474C2×#120—228no—
475C2×#120—228no—
476C22×C4⋊C4—111no—
477C22×C4⋊C4—111no—
478C22×C4⋊C4C2×D1111yescharacteristic, complemented
479C22×C22⋊C4—111no—
480C22×C22⋊C4—111no—
481C22×C22⋊C4—111no—
482C22×C22⋊C4—111no—
483C22×C22⋊C4—111no—
484C22×C22⋊C4—111no—
485C22×C22⋊C4—111no—
486C22×C22⋊C4—111no—
487C22×C22⋊C4—111no—
488C22×C22⋊C4—111no—
489C22×C22⋊C4—111no—
490C22×C22⋊C4—111no—
491C22×C22⋊C4—111no—
492C22×C22⋊C4—111no—
493C22×C22⋊C4C2×D1111yescharacteristic
494C22×C22⋊C4C2×D1111yescharacteristic
495C22×C22⋊C4C2×D1111yescharacteristic, complemented
496C22×C22⋊C4C2×D1111yescharacteristic, complemented
497#397—118no—
498#397—118no—
499#397—118no—
500#394—118no—
501#394—118no—
502#394—118no—
503#394—118no—
504#394—118no—
505#394C2×D1118yescomplemented
506#392—118no—
507#392—118no—
508#392—118no—
509#379—118no—
510C2×#95—111no—
511C2×#95—111no—
512C2×#95—111no—
513C2×#95—111no—
514C2×#95—111no—
515C2×#95C2×D1111yescharacteristic, complemented
516C22×C11—24no—
517C22×C11—24no—
518C22×C11—24no—
519C22×C11—42no—
520C22×C11—42no—
521C22×C11—42no—
522C22×C11—42no—
523C22×C11—416no—
524C22×C11—42no—
525C22×C11—42no—
526C22×C11—42no—
527C22×C11—42no—
528C22×C11—42no—
529C22×C11—42no—
530C22×C11—42no—
531C22×C11—88no—
532C22×C11#53414yes—
533C22×C11#53414yes—
534C22×C11#53414yes—
535C22×C11#56014yes—
536C22×C11#56014yes—
537C22×C11#56014yes—
538C22×C11H(3,𝔽4)14yes—
539C22×C11C23×D411yescharacteristic
540C22×C11C2×H(5,𝔽2)11yescharacteristic
541C22×C11C2×H(5,𝔽2)11yescharacteristic
542C22×C11C2×H(5,𝔽2)11yescharacteristic
543C22×C11C2×H(5,𝔽2)11yescharacteristic
544C22×C11C2×H(5,𝔽2)11yescharacteristic
545C22×C11C2×H(5,𝔽2)11yescharacteristic
546C2×D11—24no—
547C2×D11—24no—
548C2×D11—24no—
549C2×D11—24no—
550C2×D11—24no—
551C2×D11—24no—
552C2×D11—464no—
553C2×D11—42no—
554C2×D11—42no—
555C2×D11—42no—
556C2×D11—42no—
557C2×D11—42no—
558C2×D11—42no—
559C2×D11—42no—
560C2×D11—42no—
561C2×D11—416no—
562C2×D11—416no—
563C2×D11—42no—
564C2×D11—42no—
565C2×D11—42no—
566C2×D11—42no—
567C2×D11—42no—
568C2×D11—42no—
569C2×D11—42no—
570C2×D11—88no—
571C4×C11—42no—
572C4×C11—42no—
573C4×C11—42no—
574C4×C11—42no—
575C4×C11—42no—
576Dic11—42no—
577Dic11—42no—
578Dic11—42no—
579Dic11—42no—
580Dic11—42no—
581C25—111no—
582C25—111no—
583C25—118no—
584C25—114no—
585C25—111no—
586C25—442no—
587C25—442no—
588C25—442no—
589C25—442no—
590C25—442no—
591C25—442no—
592C25C22×D1111yescharacteristic
593C25C22×D1111yescharacteristic
594C22×D4—24no—
595C22×D4—42no—
596C22×D4—42no—
597C22×D4—114no—
598C22×D4—114no—
599C22×D4—114no—
600C22×D4—114no—
601C22×D4—114no—
602C22×D4—114no—
603C22×D4—224no—
604C22×D4—224no—
605C22×D4—224no—
606C22×D4—224no—
607C22×D4—224no—
608C22×D4—442no—
609C22×D4—442no—
610C22×D4—442no—
611C22×D4—442no—
612C22×D4—442no—
613C22×D4—442no—
614C22×D4—442no—
615C22×D4—442no—
616C22×D4—442no—
617C22×D4—442no—
618C22×D4—442no—
619C22×D4—442no—
620C22×D4—442no—
621C22×D4C22×D1114yes—
622C23×C4—111no—
623C23×C4—111no—
624C23×C4—111no—
625C23×C4—111no—
626C23×C4—111no—
627C23×C4C22×D1111yescharacteristic
628C23×C4C22×D1111yescharacteristic
629C23×C4C22×D1111yescharacteristic
630C23×C4C22×D1111yescharacteristic
631C23×C4C22×D1111yescharacteristic
632#120—2232no—
633#120—2232no—
634C2×C4⋊C4—42no—
635C2×C4⋊C4—114no—
636C2×C4⋊C4—114no—
637C2×C4⋊C4—442no—
638C2×C4⋊C4—442no—
639C2×C4⋊C4C22×D1114yescomplemented
640C2×C22⋊C4—24no—
641C2×C22⋊C4—42no—
642C2×C22⋊C4—42no—
643C2×C22⋊C4—42no—
644C2×C22⋊C4—114no—
645C2×C22⋊C4—114no—
646C2×C22⋊C4—114no—
647C2×C22⋊C4—114no—
648C2×C22⋊C4—114no—
649C2×C22⋊C4—114no—
650C2×C22⋊C4—114no—
651C2×C22⋊C4—114no—
652C2×C22⋊C4—114no—
653C2×C22⋊C4—114no—
654C2×C22⋊C4—114no—
655C2×C22⋊C4—114no—
656C2×C22⋊C4—114no—
657C2×C22⋊C4—114no—
658C2×C22⋊C4—224no—
659C2×C22⋊C4—224no—
660C2×C22⋊C4—224no—
661C2×C22⋊C4—224no—
662C2×C22⋊C4—224no—
663C2×C22⋊C4—442no—
664C2×C22⋊C4—442no—
665C2×C22⋊C4—442no—
666C2×C22⋊C4—442no—
667C2×C22⋊C4—442no—
668C2×C22⋊C4—442no—
669C2×C22⋊C4—442no—
670C2×C22⋊C4—442no—
671C2×C22⋊C4—442no—
672C2×C22⋊C4C22×D1114yes—
673C2×C22⋊C4C22×D1114yes—
674C2×C22⋊C4C22×D1114yescomplemented
675C2×C22⋊C4C22×D1114yescomplemented
676#95—114no—
677#95—114no—
678#95—114no—
679#95—114no—
680#95—114no—
681#95C22×D1114yescomplemented
682C2×C11—44no—
683C2×C11—82no—
684C2×C11#281218yescomplemented
685C2×C11C2×#53411yescharacteristic
686C2×C11C2×#53411yescharacteristic
687C2×C11C2×#53411yescharacteristic
688C2×C11C2×#56011yescharacteristic
689C2×C11C2×#56011yescharacteristic
690C2×C11C2×#56011yescharacteristic
691C2×C11C2×H(3,𝔽4)11yescharacteristic
692D11—44no—
693D11—44no—
694D11—82no—
695C24—22no—
696C24—22no—
697C24—22no—
698C24—22no—
699C24—22no—
700C24—22no—
701C24—22no—
702C24—22no—
703C24—22no—
704C24—22no—
705C24—22no—
706C24—22no—
707C24—22no—
708C24—114no—
709C24—114no—
710C24—112no—
711C24—112no—
712C24—1116no—
713C24—112no—
714C24—222no—
715C24—222no—
716C24—222no—
717C24—222no—
718C24—222no—
719C24—222no—
720C24—222no—
721C24—222no—
722C24—222no—
723C24—222no—
724C24—222no—
725C24—222no—
726C24—222no—
727C24—222no—
728C24—222no—
729C24—222no—
730C24—222no—
731C24—222no—
732C24—222no—
733C24—4416no—
734C24—4416no—
735C24—4416no—
736C24—444no—
737C24—444no—
738C24—444no—
739C24—444no—
740C24—444no—
741C24—444no—
742C24—4416no—
743C24—4416no—
744C24—4416no—
745C24—4416no—
746C24D4×D1114yes—
747C24C23×D1112yes—
748C24C23×D1112yes—
749C24C23×D1111yescharacteristic
750C2×D4—28no—
751C2×D4—44no—
752C2×D4—44no—
753C2×D4—416no—
754C2×D4—228no—
755C2×D4—228no—
756C2×D4—228no—
757C2×D4—228no—
758C2×D4—228no—
759C2×D4—444no—
760C2×D4—444no—
761C2×D4—444no—
762C2×D4—444no—
763C2×D4—4416no—
764C2×D4—4416no—
765C2×D4—444no—
766C2×D4—444no—
767C2×D4—444no—
768C2×D4—444no—
769C2×D4—444no—
770C2×D4—444no—
771C2×D4—444no—
772C2×D4—444no—
773C2×D4—444no—
774C2×D4—4416no—
775C2×D4—4416no—
776C2×D4—4416no—
777C2×D4—4416no—
778C22×C4—22no—
779C22×C4—22no—
780C22×C4—22no—
781C22×C4—22no—
782C22×C4—22no—
783C22×C4—22no—
784C22×C4—22no—
785C22×C4—22no—
786C22×C4—22no—
787C22×C4—22no—
788C22×C4—22no—
789C22×C4—22no—
790C22×C4—22no—
791C22×C4—22no—
792C22×C4—22no—
793C22×C4—112no—
794C22×C4—112no—
795C22×C4—112no—
796C22×C4—112no—
797C22×C4—112no—
798C22×C4—222no—
799C22×C4—222no—
800C22×C4—222no—
801C22×C4—222no—
802C22×C4—222no—
803C22×C4—222no—
804C22×C4—222no—
805C22×C4—222no—
806C22×C4—222no—
807C22×C4—222no—
808C22×C4—222no—
809C22×C4—222no—
810C22×C4—222no—
811C22×C4—222no—
812C22×C4—222no—
813C22×C4C23×D1112yes—
814C22×C4C23×D1112yes—
815C22×C4C23×D1112yes—
816C22×C4C23×D1112yes—
817C22×C4C23×D1112yes—
818C4⋊C4—44no—
819C4⋊C4—444no—
820C4⋊C4—444no—
821C22⋊C4—28no—
822C22⋊C4—44no—
823C22⋊C4—44no—
824C22⋊C4—44no—
825C22⋊C4—228no—
826C22⋊C4—228no—
827C22⋊C4—228no—
828C22⋊C4—228no—
829C22⋊C4—228no—
830C22⋊C4—444no—
831C22⋊C4—444no—
832C22⋊C4—444no—
833C22⋊C4—444no—
834C22⋊C4—444no—
835C22⋊C4—444no—
836C22⋊C4—444no—
837C22⋊C4—444no—
838C22⋊C4—444no—
839C11C2×#281211yescharacteristic, complemented, Sylow
840C23—28no—
841C23—28no—
842C23—28no—
843C23—22no—
844C23—22no—
845C23—22no—
846C23—22no—
847C23—22no—
848C23—22no—
849C23—22no—
850C23—22no—
851C23—22no—
852C23—22no—
853C23—22no—
854C23—22no—
855C23—22no—
856C23—44no—
857C23—44no—
858C23—44no—
859C23—44no—
860C23—44no—
861C23—44no—
862C23—44no—
863C23—44no—
864C23—44no—
865C23—44no—
866C23—44no—
867C23—114no—
868C23—114no—
869C23—228no—
870C23—228no—
871C23—228no—
872C23—228no—
873C23—228no—
874C23—228no—
875C23—222no—
876C23—222no—
877C23—222no—
878C23—222no—
879C23—222no—
880C23—222no—
881C23—222no—
882C23—222no—
883C23—222no—
884C23—222no—
885C23—222no—
886C23—222no—
887C23—222no—
888C23—222no—
889C23—222no—
890C23—222no—
891C23—222no—
892C23—222no—
893C23—222no—
894C23—4416no—
895C23—4416no—
896C23—4416no—
897C23—4416no—
898C23—4416no—
899C23—4416no—
900C23—4416no—
901C23—44128no—
902C23—444no—
903C23—444no—
904C23—444no—
905C23—444no—
906C23—444no—
907C23—444no—
908C23—444no—
909C23—444no—
910C23—444no—
911C23—444no—
912C23—444no—
913C23—444no—
914C23—444no—
915C23—444no—
916C23—444no—
917C23C2×D4×D1114yes—
918C23C2×D4×D1112yes—
919C23#6703712yes—
920C23#6703712yes—
921C23#6703712yes—
922C23#6704212yes—
923C23#6704212yes—
924C23#6704212yes—
925C23C24×D1111yescharacteristic
926D4—416no—
927D4—4416no—
928D4—4416no—
929D4—4416no—
930D4—4416no—
931D4—4416no—
932D4—4416no—
933C2×C4—22no—
934C2×C4—22no—
935C2×C4—22no—
936C2×C4—22no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—22no—
944C2×C4—22no—
945C2×C4—22no—
946C2×C4—22no—
947C2×C4—22no—
948C2×C4—44no—
949C2×C4—44no—
950C2×C4—44no—
951C2×C4—44no—
952C2×C4—44no—
953C2×C4—222no—
954C2×C4—222no—
955C2×C4—222no—
956C2×C4—222no—
957C2×C4—222no—
958C2×C4—222no—
959C2×C4—222no—
960C2×C4—222no—
961C2×C4—222no—
962C2×C4—222no—
963C2×C4—222no—
964C2×C4—222no—
965C2×C4—222no—
966C2×C4—222no—
967C2×C4—222no—
968C2×C4—444no—
969C2×C4—444no—
970C2×C4—444no—
971C2×C4—444no—
972C2×C4—444no—
973C22—24no—
974C22—24no—
975C22—24no—
976C22—42no—
977C22—42no—
978C22—42no—
979C22—42no—
980C22—416no—
981C22—42no—
982C22—42no—
983C22—42no—
984C22—42no—
985C22—42no—
986C22—42no—
987C22—42no—
988C22—88no—
989C22—224no—
990C22—224no—
991C22—224no—
992C22—224no—
993C22—224no—
994C22—224no—
995C22—4464no—
996C22—442no—
997C22—442no—
998C22—442no—
999C22—442no—
1000C22—442no—
1001C22—442no—
1002C22—442no—
1003C22—442no—
1004C22—4416no—
1005C22—4416no—
1006C22—442no—
1007C22—442no—
1008C22—442no—
1009C22—442no—
1010C22—442no—
1011C22—442no—
1012C22—442no—
1013C22—888no—
1014C22#1062312014yes—
1015C22#1062313614yes—
1016C22#1062315114yes—
1017C22#1062315114yes—
1018C22#1062318414yes—
1019C22#1062319714yes—
1020C22#1062321414yes—
1021C22C22×D4×D1111yescharacteristic
1022C22C2×#6703711yescharacteristic
1023C22C2×#6703711yescharacteristic
1024C22C2×#6703711yescharacteristic
1025C22C2×#6704211yescharacteristic
1026C22C2×#6704211yescharacteristic
1027C22C2×#6704211yescharacteristic
1028C4—42no—
1029C4—42no—
1030C4—42no—
1031C4—42no—
1032C4—42no—
1033C4—442no—
1034C4—442no—
1035C4—442no—
1036C4—442no—
1037C4—442no—
1038C2—44no—
1039C2—82no—
1040C2—444no—
1041C2—444no—
1042C2—882no—
1043C2#1307661218yesdirect product factor
1044C2C2×#1062313611yescharacteristic
1045C2C2×#1062312011yescharacteristic
1046C2C2×#1062318411yescharacteristic
1047C2C2×#1062315111yescharacteristic
1048C2C2×#1062315111yescharacteristic
1049C2C2×#1062319711yescharacteristic
1050C2C2×#1062321411yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#394C2
socleC24×C11C24
hypercenterC2×#394D11
hypocenterC11C2×#2812
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#394

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C22×#66935C2semidirect
2. C22×#66990C2semidirect
3. #13076612C2direct (N × H)
4. C2×#10622565C2semidirect
5. C2×#10622287C2semidirect
6. C2×#10622606C2semidirect
7. C2×#10622285C2semidirect
8. C2×#10622604C2semidirect
9. C2×#10622574C2semidirect
10. C2×#10622574C2semidirect
11. C2×#10622572C2semidirect
12. C2×#10622573C2semidirect
13. C2×#10622573C2semidirect
14. C2×#10622836C2semidirect
15. C2×#10622568C2semidirect
16. C2×C11×#394C2semidirect
22. C23×C22⋊D11C22semidirect
25. C22×C11×C4⋊C4C22semidirect
28. C22×C11×C22⋊C4C22semidirect
29. C22×C11×C22⋊C4C22semidirect
32. C22×C22⋊Dic11C22semidirect
34. C2×#66990C22semidirect
43. C22×(C2×D11)⋊C4C22semidirect
44. C22×(C2×D11)⋊C4C22semidirect
45. C22×(C2×D11)⋊C4C22semidirect
46. C22×C4⋊Dic11C22semidirect
47. C22×Dic11⋊C4C22semidirect
49. C2×#66935C22semidirect
50. C11×#394C22semidirect
51. C2×C11×#95C22semidirect
52. #10622836C22semidirect
53. C2×C11⋊#95C22semidirect
54. C2×C11⋊#95C22semidirect
55. C2×C11⋊#95C22semidirect
56. C2×C11⋊#95C22semidirect
57. C2×C11⋊#95C22semidirect
58. #10622606C22semidirect
59. #10622604C22semidirect
60. #10622574C22semidirect
61. #10622574C22semidirect
62. #10622573C22semidirect
63. #10622573C22semidirect
64. #10622572C22semidirect
65. #10622568C22semidirect
66. #10622565C22semidirect
67. #10622287C22semidirect
68. #10622285C22semidirect
77. C24×D11D4semidirect
106. C22×C22⋊D11C23semidirect
121. C2×C11×C4⋊C4C23semidirect
128. C2×C11×C22⋊C4C23semidirect
129. C2×C11×C22⋊C4C23semidirect
135. C2×C22⋊Dic11C23semidirect
156. C2×(C2×D11)⋊C4C23semidirect
157. C2×(C2×D11)⋊C4C23semidirect
158. C2×(C2×D11)⋊C4C23semidirect
160. C2×C4⋊Dic11C23semidirect
162. C2×Dic11⋊C4C23semidirect
164. C11×#95C23semidirect
165. C11⋊#95C23semidirect
166. C11⋊#95C23semidirect
167. C11⋊#95C23semidirect
168. C11⋊#95C23semidirect
169. C11⋊#95C23semidirect
222. C23×D11C2×D4semidirect
326. C2×#394D11semidirect
478. C22×C4⋊C4C2×D11semidirect
495. C22×C22⋊C4C2×D11semidirect
496. C22×C22⋊C4C2×D11semidirect
505. #394C2×D11semidirect
515. C2×#95C2×D11semidirect
639. C2×C4⋊C4C22×D11semidirect
674. C2×C22⋊C4C22×D11semidirect
675. C2×C22⋊C4C22×D11semidirect
681. #95C22×D11semidirect
684. C2×C11#2812semidirect
839. C11C2×#2812semidirect
1043. C2#13076612direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×#669352
C22×#669902
#130766122
C2×#106225652
C2×#106222872
C2×#106226062
C2×#106222852
C2×#106226042
C2×#106225742
C2×#106225722
C2×#106225732
C2×#106228362
C2×#106225682
C2×C11×#3942
C2×#281211